Asubway train starts from rest at a station and accelerates uniformly at 1.8m/s^2 for 15 sec. then it runs at a constant speed for the next 35 sec. before decelerating at 2.0m/s^2 until it comes to rest at the next station. find the distance between the stations and the average speed of the train.
( show step by step and the formula that is used. you! )

This looks so scary just because there are so many parts to it.
Take them one at a time:

First piece:
From rest, accelerates 1.8 m/s² for 15 sec.
Speed at the end of the 15 sec = 1.8 x 15 = 27 m/s
Distance covered = (average speed) x (time) = (13.5) x (15) = 202.5 meters

Middle piece:
Starts this piece at 27 m/s.
Runs at constant speed for 35 sec.
Covers (27 x 35) = 945 meters
Finishes this piece (15 + 35) = 50 seconds after leaving the first station
Finishes this piece (202.5 + 945) = 1147.5 meters from the first station.

Last piece:
Starts this piece 50 seconds after leaving the first station,
         1147.5 meters from it, still moving at 27 m/s.
Decelerates at 2.0 m/s² .
--> It takes 27/2.0 = 13.5 seconds to come to a stop.
--> Distance covered during this piece = (average speed) x (time)
           = (13.5 m/s) x (13.5 sec) = 182.25 meters
Finishes this piece (50 + 13.5) = 63.5 seconds after leaving the first station
Finishes this piece (1147.5 + 182.25) = 1,329.75 m from the first station  

Distance between the stations (along the track) = 1,329.75 meters.

Average speed = (total distance) / (total time) = 1,329.75 / 63.5 = 20.941 m/s.

I sure hope I didn't make any stupid arithmetic blunders here,
because I really don't feel like going back and checking it.
Let me know, and I'll fix them.